Darryn Randall collapsed and was taken to hospital where medical staff were unable to revive him.
He was just 32 years old.
Randall was hit after he attempted to pull a short delivery while playing for Old Selbornians against Fort Hare University.
He had played first-class matches for Border and is survived by his mother and his fiancee.
Cricket South Africa chief executive Haroon Lorgat expressed the federation's condolences and said it would be offering counselling to those involved in the match.
"This is a very sad day, indeed," Lorgat said of the incident.
"I would like to convey CSA's deepest condolences on behalf of the South African cricketing family not just to his family and friends but also to all the players, umpires, clubs and everybody else who was present at this match.
"CSA will be offering counselling to all those involved."
Randall represented Border at youth and senior provincial levels and ran a primary-school cricket academy.